Ensuring mechanical reliability is one of the key concerns for printed circuit board (PCB) design. Accurate reliability analysis requires the ability to predict the warpage (displacement) of PCBs under thermo-mechanical loads. PCBs are very complex, consisting of multiple layers of dielectric material and metal conductors. For example, a PCB may include strips of metal (also called traces) and Fr4 materials (e.g., composite materials composed of woven fiberglass cloth with an epoxy resin binder). There may be hundreds of conductors and these may have very complicated shapes. The conductors may be polygons with hundreds of vertices. In addition, these polygons may overlap, may contain polygonal holes and may have a very high aspect ratio.
Conventional methods based on Finite Element Analysis (FEA) rely on accurate modeling of the board and conductor geometry to predict displacement. However, due to the complexity of the geometry, the FEA approach becomes computationally prohibitive.